Method and apparatus for sub-sampling of a codebook in LTE-A system

ABSTRACT

The embodiments of the present invention disclose a method and an apparatus for sub-sampling of a codebook in the LTE-A system where a precoding matrix W is a product of two matrices W 1  and W 2 , i.e. W=W 1 W 2 , codebooks for W, W 1  and W 2  are denoted as C, C 1  and C 2  respectively, and r indicates a rank. The method includes sub-sampling the codebook C such that the sub-sampled codebook C has a size of equal to or less than 4 bits. In the sub-sampling, codewords evenly distributed in the codebook C are extracted, where some or all of the codewords are in a form of discrete Fourier transform (DFT) vector to be suitable for evenly linear arrays, and the other codewords are suitable for cross-polarized linear arrays.

TECHNICAL FIELD

The present invention relates to Long Term Evolution Advanced (LTE-A), especially to a method and apparatus for sub-sampling of a codebook in LTE-A system.

BACKGROUND OF THE INVENTION

Nowadays, LTE technology is one of leading technologies in the field of radio technology. Various precoding technologies are widely used in the LTE system. In accordance with the 8 transmitting antenna codebook prescribed in R1-105011 of LTE-A Rel-10 (8Tx codebook for short), a precoder for subbands is a product of two matrices W₁ and W₂, in which matrix W₁ corresponds to wideband and/or long-term channel properties, and the other matrix W₂ corresponds to frequency-selective and/or short-term channel properties. For rank 1 and rank 2, the codebook sizes for W₁ and W₂ are both 4 bits. Thus, in Channel State Information (CSI) reporting mode 1-1 (broadband mode), 8 bits are needed to represent Precoding Matrix Indicator (PMI), however, it is prescribed that only 4 bits could be used for PMI feedback. Thus, the currently prescribed 8Tx codebook cannot be directly used in this CSI reporting mode 1-1, and thus sub-sampling of the currently prescribed 8Tx codebook is necessary and important.

In R1-105011, “Way Forward on 8Tx Codebook for Rel.10 DL MIMO”, RAN1#62, Madrid, Spain, August 2010, it is prescribed only the 8Tx codebook, while no solution is presented for sub-sampling of the 8Tx codebook.

SUMMARY OF THE INVENTION

In view of the problems existing in the prior art, the embodiments of the present invention provide a method and an apparatus for sub-sampling of a codebook in the LTE-A system.

According to an embodiment of the invention, it is provided a method for sub-sampling of a codebook in a LTE-A system where a precoding matrix W is a product of two matrices W₁ and W₂, i.e. W=W₁W₂, codebooks for W, W₁ and W₂ are denoted as C, C₁ and C₂ respectively, and r indicates a rank. The method comprises:

sub-sampling the codebook C such that the sub-sampled codebook C has a size of equal to or less than 4 bits.

According to another embodiment of the invention, it is provided an apparatus for sub-sampling of a codebook in a LTE-A system where a precoding matrix W is a product of two matrices W₁ and W₂, i.e. W=W₁W₂, codebooks for W, W₁ and W₂ are denoted as C, C₁ and C₂ respectively, and r indicates a rank. The apparatus comprises:

sub-sampling means for sub-sampling the codebook C such that the sub-sampled codebook C has a size of equal to or less than 4 bits.

BRIEF DESCRIPTION OF THE INVENTION

The other features, objects and advantages of this invention are made more evident, when the following detailed description to the non-limiting embodiments is read in conjunction with the accompanying drawings.

FIG. 1 illustrates a method for sub-sampling of a codebook in a LTE-A system according to an embodiment of the invention.

FIG. 2 illustrates an apparatus for sub-sampling of a codebook in a LTE-A system according to an embodiment of the invention.

DETAILED DESCRIPTION

A method and an apparatus for sub-sampling of a codebook in the LTE-A system is described in conjunction with drawings and with reference to the embodiments.

Prior to introducing embodiments of the invention, let's have a review to the 8Tx codebook C presented in R1-105011 of LTE-A Rel-10, in which the precoding matrix W is defined as a product of W₁ and W₂, i.e., W=W₁W₂. Codebooks for W, W₁ and W₂ are denoted as C, C₁ and C₂ respectively. In other words, the 8Tx codebook C is comprised of two constituent codebooks (namely, codebooks C₁ and C₂).

A first Codebook1 C₁ of rank 1 codebook and rank 2 codebook may be expressed as:

$\mspace{20mu}{{B = \begin{bmatrix} b_{0} & b_{1} & \ldots & b_{31} \end{bmatrix}},{\lbrack B\rbrack_{{1 + m},{1 + n}} = {\mathbb{e}}^{j\frac{\;{2\pi\;{mn}}}{32}}},{m = 0},1,2,3,\mspace{20mu}{n = 0},1,\ldots\mspace{14mu},31}$ $X^{(k)} \in \left\{ {{{\begin{bmatrix} b_{2k\;{mod}\; 32} & b_{{({{2k} + 1})}{mod}\; 32} & b_{{({{2k} + 2})}{mod}\; 32} & b_{{({{2k} + 3})}{mod}\; 32} \end{bmatrix}\text{:}k} = 0},1,\ldots\mspace{14mu},15} \right\}$ $\mspace{20mu}{W_{1}^{(k)} = \begin{bmatrix} X^{(k)} & 0 \\ 0 & {X^{(k)}\;} \end{bmatrix}}$

Codebook 1: C₁={W₁ ⁽⁰⁾, W₁ ⁽¹⁾, W₁ ⁽²⁾, . . . , W₁ ⁽¹⁵⁾}

A second Codebook2 C₂ of rank 1 codebook may be expressed as:

${W_{2}^{({{4k} + l})} = {\frac{1}{\sqrt{2}}\begin{bmatrix} e_{k + 1} \\ {\alpha_{l}e_{k + 1}} \end{bmatrix}}},{k = 0},1,2,{3;{l = 0}},1,2,3$

Codebook 2: C₂={W₂ ⁽⁰⁾, W₂ ⁽¹⁾, W₂ ⁽²⁾, . . . , W₂ ⁽¹⁵⁾},

where α₀=1, α₁=j, α₂=−1, α₃=−j, e_(k) is an 4×1 selection vector for which the k-th element has a value of 1 and other elements are all zero.

A second codebook Codebook2 C₂ of rank 2 codebook may be expressed as:

${W_{2}^{({{2k} + l})} = {\frac{1}{\sqrt{2}}\begin{bmatrix} Y_{1}^{k} & Y_{2}^{k} \\ {\alpha_{l}Y_{1}^{k}} & {{- \alpha_{l}}Y_{2}^{k}} \end{bmatrix}}},{k = 0},1,\ldots\mspace{14mu},{7;{l = 0}},1$

Codebook 2: C₂={W₂ ⁽⁰⁾, W₂ ⁽¹⁾, W₂ ⁽²⁾, . . . , W₂ ⁽¹⁵⁾},

where α₀=1, α₁=j, e_(k) is an 4×1 selection vector for which the k-th element has a value of 1 and other elements are all zero, and

(Y₁ ⁰,Y₂ ⁰)=(e₁,e₁), (Y₁ ¹,Y₂ ¹)=(e₂,e₂), (Y₁ ²,Y₂ ²)=(e₃,e₃), (Y₁ ³,Y₂ ³)=(e₄,e₄), (Y₁ ⁴,Y₂ ⁴)=(e₁,e₂), (Y₁ ⁵,Y₂ ⁵)=(e₂,e₃), (Y₁ ⁶,Y₂ ⁶)=(e₁,e₄), (Y₁ ⁷,Y₂ ⁷)=(e₂,e₄).

A first codebook Codebook1 C₁ of rank 3 codebook and rank 4 codebook presented in R1-105011 may be expressed as:

${B = \begin{bmatrix} b_{0} & b_{1} & \ldots & b_{15} \end{bmatrix}},{\lbrack B\rbrack_{{1 + m},{1 + n}} = {\mathbb{e}}^{j\frac{\;{2\pi\;{mn}}}{16}}},{m = 0},1,2,3,{n = 0},1,{\ldots\mspace{14mu} 15}$ $X^{(k)} \in \left\{ {{{\begin{bmatrix} b_{4k\;{mod}\; 32} & b_{{({{4k} + 1})}{mod}\; 32} & \ldots & b_{{({{4k} + 7})}{mod}\; 16} \end{bmatrix}\text{:}k} = 0},1,2,3} \right\}$ $W_{1}^{(k)} = \begin{bmatrix} X^{(k)} & 0 \\ 0 & {X^{(k)}\;} \end{bmatrix}$

Codebook 1: C₁={W₁ ⁽⁰⁾, W₁ ⁽¹⁾, W₁ ⁽²⁾, W₁ ⁽³⁾}.

A second codebook Codebook2 C₂ of rank 3 codebook may be expressed as:

$\mspace{20mu}{{W_{2} \in C_{2}} = \left\{ {\frac{1}{\sqrt{2}}\begin{bmatrix} Y_{1} & Y_{2} \\ Y_{1} & {- Y_{2}} \end{bmatrix}} \right\}}$ ${\left( {Y_{1},Y_{2}} \right) \in \begin{Bmatrix} {\left( {e_{1},\begin{bmatrix} e_{1} & e_{5} \end{bmatrix}} \right),\left( {e_{2},\begin{bmatrix} e_{2} & e_{6} \end{bmatrix}} \right),\left( {e_{3},\begin{bmatrix} e_{3} & e_{7} \end{bmatrix}} \right),\left( {e_{4},\begin{bmatrix} e_{4} & e_{8} \end{bmatrix}} \right),} \\ {\left( {e_{5},\begin{bmatrix} e_{1} & e_{5} \end{bmatrix}} \right),\left( {e_{6},\begin{bmatrix} e_{2} & e_{6} \end{bmatrix}} \right),\left( {e_{7},\begin{bmatrix} e_{3} & e_{7} \end{bmatrix}} \right),\left( {e_{8},\begin{bmatrix} e_{4} & e_{8} \end{bmatrix}} \right),} \\ {\left( {\begin{bmatrix} e_{1} & e_{5} \end{bmatrix},e_{5}} \right),\left( {\begin{bmatrix} e_{2} & e_{6} \end{bmatrix},e_{6}} \right),\left( {\begin{bmatrix} e_{3} & e_{7} \end{bmatrix},e_{7}} \right),\left( {\begin{bmatrix} e_{4} & e_{8} \end{bmatrix},e_{8}} \right),} \\ {\left( {\begin{bmatrix} e_{5} & e_{1} \end{bmatrix},e_{1}} \right),\left( {\begin{bmatrix} e_{6} & e_{2} \end{bmatrix},e_{2}} \right),\left( {\begin{bmatrix} e_{7} & e_{3} \end{bmatrix},e_{3}} \right),\left( {\begin{bmatrix} e_{8} & e_{4} \end{bmatrix},e_{4}} \right)} \end{Bmatrix}};$

A second codebook Codebook2 C₂ of rank 4 codebook may be expressed as:

${W_{2} \in C_{2}} = \left\{ {{\frac{1}{\sqrt{2}}\begin{bmatrix} Y & Y \\ Y & {- Y} \end{bmatrix}},{\frac{1}{\sqrt{2}}\begin{bmatrix} Y & Y \\ {jY} & {- {jY}} \end{bmatrix}}} \right\}$ $Y \in {\left\{ {\begin{bmatrix} e_{1} & e_{5} \end{bmatrix},\begin{bmatrix} e_{2} & e_{6} \end{bmatrix},\begin{bmatrix} e_{3} & e_{7} \end{bmatrix},\begin{bmatrix} e_{4} & e_{8} \end{bmatrix}} \right\}.}$

In the context of the application, e_(k) indicates a 4×1 selection vector for which the k-th element has a value of 1 and other elements are all zero, unless otherwise indicated.

As to rank 5-8 codebooks presented in R1-105011, no sub-sampling is required in CSI reporting mode 1-1. Therefore, detailed description for it is omitted here. As to rank 5-8 codebooks, please refer to R1-105011 for more information.

Payload sizes for rank 1-8 codebooks are summarizes as follows.

If the rank is 1 or 2, C₁ has a size of 4 bits, and C₂ has a size of 4 bits;

If the rank is 3, C₁ has a size of 2 bits, and C₂ has a size of 4 bits;

If the rank is 4, C₁ has a size of 2 bits, and C₂ has a size of 3 bits;

If the rank is 5-7, C₁ has a size of 2 bits, and C₂ has a size of 0 bit;

If the rank is 8, C₁ has a size of 0 bit, and C₂ has a size of 0 bit.

With regard to CSI reporting mode 1-1, only 4 bits may be used for feeding back W₁ and W₂. Thus, in CSI reporting mode 1-1, rank 1-4 codebooks should be sub-sampled to 4 bits at most.

FIG. 1 illustrates a method for sub-sampling of a codebook in the LTE-A system according to an embodiment of the invention. In the system, a precoding matrix W is a product of two matrices W₁ and W₂, i.e. W=W₁W₂, codebooks for W, W₁ and W₂ are denoted as C, C₁ and C₂ respectively, and r indicates a rank. As shown in FIG. 1, in method 100 at step 101, a codebook C is sub-sampled such that the sub-sampled codebook C has a size of equal to or less than 4 bits. Codebook C is a 8Tx codebook prescribed in R1-105011, for example. When the rank is 1 or 2, the codebook C has a size of 8 bits, i.e., it contains 256 codewords. After the sub-sampling, 16 codewords evenly distributed in the codebook C are extracted from the 256 codewords such that the sub-sampled codebook C may represent PMI with 4 bits.

According to an embodiment of the invention, when r=3 or 4, C₁ still has the size of 2 bits, but C₂ is sub-sampled as:

$\begin{matrix} {{{C_{2} = {{\left\{ {\frac{1}{\sqrt{2}}\begin{bmatrix} Y_{1} & Y_{2} \\ Y_{1} & {- Y_{2}} \end{bmatrix}} \right\}\mspace{14mu}{for}\mspace{14mu} r} = 3}}\left( {Y_{1},Y_{2}} \right) \in \left\{ {\left( {e_{1},\left\lbrack {e_{1},e_{5}} \right\rbrack} \right),\left( {e_{2},\left\lbrack {e_{2},e_{6}} \right\rbrack} \right),\left( {e_{3},\left\lbrack {e_{3},e_{7}} \right\rbrack} \right),\left( {e_{4}\left\lbrack {e_{4},e_{8}} \right\rbrack} \right)} \right\}};} & (1) \\ {{C_{2} = {{\left\{ {\frac{1}{\sqrt{2}}\begin{bmatrix} Y & Y \\ Y & {- Y} \end{bmatrix}} \right\}\mspace{14mu}{for}\mspace{14mu} r} = 4}}{{Y \in \begin{Bmatrix} {\left\lbrack {e_{1},e_{5}} \right\rbrack,\left\lbrack {e_{2},e_{6}} \right\rbrack,} \\ {\left\lbrack {e_{3},e_{7}} \right\rbrack,\left\lbrack {e_{4},e_{8}} \right\rbrack} \end{Bmatrix}};}} & (2) \end{matrix}$ where e_(k) indicates a 4×1 selection vector for which the k-th element has a value of 1 and other elements are all zero. It can be seen that the above sub-sampled rank 3 codebook and rank 4 codebook both have a nesting property.

According to another embodiment of the invention, when r=1 or 2, C₁ still has the size of 4 bits, but C₂ is defined as:

the sub-sampled C₂ is

${C_{2} = {{\left\{ \begin{bmatrix} e_{1} \\ e_{1} \end{bmatrix} \right\}\mspace{14mu}{for}\mspace{14mu} r} = 1}},$

the sub-sampled C₂ is

${C_{2} = {{\left\{ \begin{bmatrix} e_{1} & e_{1} \\ e_{1} & {- e_{1}} \end{bmatrix} \right\}\mspace{14mu}{for}\mspace{14mu} r} = 2}},$ where the sub-sampled rank 1 codebook, rank 2 codebook as well as the above sub-sampled rank 3 codebook and rank 4 codebook all have a nesting property.

According to a further embodiment of the invention, when r=1 or 2, C₁ still has the size of 4 bits. For each codeword in C₁, only one codeword in C₂ is corresponding thereto. According to a preferred embodiment of the invention, when r=1, for the codeword W₁ ^((4k+l)), (k=0, 1, 2, 3, l=0, 1, 2, 3) in C₁, the codeword

$\frac{1}{\sqrt{2}}\begin{bmatrix} e_{1} \\ {\alpha_{l}e_{1}} \end{bmatrix}$ in C₂ is extracted to correspond thereto, where α₀=1, α₁=j, α₂=−1 and α₃=−j. When r=2, for the codeword W₁ ^((2k+l)) (k=0, 1, . . . , 7, l=0, 1) in C₁, the codeword

$\frac{1}{\sqrt{2}}\begin{bmatrix} e_{1} & e_{1} \\ {\alpha_{l}e_{1}} & {{- \alpha_{l}}e_{1}} \end{bmatrix}$ in C₂ is extracted to correspond thereto, where α₀=1, α₁=j.

According to another embodiment of the invention, when r=1 or 2, C₁ and C₂ are sub-sampled respectively. In particular, C₁ is sub-sampled to 3 bits, and C₂ is sub-sampled to 1 bit. According to a preferred embodiment of the invention, the sub-sampled C₁ is C₁={W₁ ⁽⁰⁾, W₁ ⁽²⁾, W₁ ⁽⁴⁾, . . . , W₁ ⁽¹⁴⁾}, the sub-sampled C₂ is

${C_{2} = {{\left\{ {\begin{bmatrix} e_{1} \\ e_{1} \end{bmatrix},\begin{bmatrix} e_{1} \\ {j\; e_{1}} \end{bmatrix}} \right\}\mspace{14mu}{for}\mspace{14mu} r} = 1}};$ and the sub-sampled C₂ is

$C_{2} = {{\left\{ {\begin{bmatrix} e_{1} & e_{1} \\ e_{1} & {- e_{1}} \end{bmatrix},\begin{bmatrix} e_{1} & e_{1} \\ {j\; e_{1}} & {{- j}\; e_{1}} \end{bmatrix}} \right\}\mspace{14mu}{for}\mspace{14mu} r} = 2.}$

According to another embodiment of the invention, in the sub-sampling, codewords evenly distributed in the codebook C are extracted, where some or all of the codewords are in a form of discrete Fourier transform (DFT) vector to be suitable for evenly linear arrays, and the other codewords are suitable for cross-polarized linear arrays.

FIG. 2 illustrates an apparatus 200 for sub-sampling of a codebook in the LTE-A system according to an embodiment of the invention. In the system, a precoding matrix W is a product of two matrices W₁ and W₂, i.e. W=W₁W₂, codebooks for W, W₁ and W₂ are denoted as C, C₁ and C₂ respectively, and r indicates a rank. As shown in FIG. 2, the apparatus 200 includes a sub-sampling means 201 adapted to sub-sample a codebook C such that the sub-sampled codebook C has a size of equal to or less than 4 bits.

According to an embodiment of the invention, when r=3 or 4, C₁ still has the size of 2 bits, and C₂ is sub-sampled as:

$\begin{matrix} {{{{C_{2} = {{\left\{ {\frac{1}{\sqrt{2}}\begin{bmatrix} Y_{1} & Y_{2} \\ Y_{1} & {- Y_{2}} \end{bmatrix}} \right\}\mspace{14mu}{for}\mspace{14mu} r} = 3}}\left( {Y_{1},Y_{2}} \right) \in \left\{ {\left( {e_{1},\left\lbrack {e_{1},e_{5}} \right\rbrack} \right),\left( {e_{2}\left\lbrack {e_{2},e_{6}} \right\rbrack} \right),\left( {e_{3},\left\lbrack {e_{3},e_{7}} \right\rbrack} \right),\left( {e_{4},\left\lbrack {e_{4},e_{8}} \right\rbrack} \right)} \right\}};}{C_{2} = {{\left\{ {\frac{1}{\sqrt{2}}\begin{bmatrix} Y & Y \\ Y & {- Y} \end{bmatrix}} \right\}\mspace{14mu}{for}\mspace{14mu} r} = 4}}{{Y \in \left\{ {\left\lbrack {e_{1},e_{5}} \right\rbrack,\left\lbrack {e_{2},e_{6}} \right\rbrack,\left\lbrack {e_{3},e_{7}} \right\rbrack,\left\lbrack {e_{4},e_{8}} \right\rbrack} \right\}};}} & (3) \end{matrix}$ where e_(k) indicates a 4×1 selection vector for which the k-th element has a value of 1 and other elements are all zero. It can be seen that the above sub-sampled rank 3 codebook and rank 4 codebooks both have a nesting property.

According to an embodiment of the invention, when r=1 or 2, C₁ still has the size of 4 bits, but C₂ is defined as:

the sub-sampled C₂ is

${C_{2} = {{\left\{ \begin{bmatrix} e_{1} \\ e_{1} \end{bmatrix} \right\}\mspace{14mu}{for}\mspace{14mu} r} = 1}},$

the sub-sampled C₂ is

${C_{2} = {{\left\{ \begin{bmatrix} e_{1} & e_{1} \\ e_{1} & {- e_{1}} \end{bmatrix} \right\}\mspace{14mu}{for}\mspace{14mu} r} = 2}},$ where the sub-sampled rank 1 codebook, rank 2 codebook as well as the above sub-sampled rank 3 codebook and rank 4 codebook have a nesting property.

According to an embodiment of the invention, when r=1 or 2, C₁ still has the size of 4 bits. For each codeword in C₁, only one codeword in C₂ is corresponding thereto. According to a preferred embodiment of the invention, when r=1, for the codeword W₁ ^((4k+l)) (k=0, 1, 2, 3, l=0, 1, 2, 3) in C₁, the codeword

$\frac{1}{\sqrt{2}}\begin{bmatrix} e_{1} \\ {\alpha_{l}e_{1}} \end{bmatrix}$ in C₂ is extracted to correspond thereto, where α₀=1, α₁=j, α₂=−1 and α₃=−j. When r=2, for the codeword w₁ ^((2k+l)) (k=0, 1, . . . , 7, l=0, 1) in C₁, the codeword

$\frac{1}{\sqrt{2}}\begin{bmatrix} e_{1} & e_{1} \\ {\alpha_{l}e_{1}} & {{- \alpha_{l}}e_{1}} \end{bmatrix}$ in C₂ is extracted to correspond thereto, where α₀=1, α₁=j.

According to an embodiment of the invention, when r=1 or 2, C₁ and C₂ are sub-sampled respectively. In particular, C₁ is sub-sampled to 3 bits, and C₂ is sub-sampled to 1 bit. According to a preferred embodiment of the invention, the sub-sampled C₁ is C₁={W₁ ⁽⁰⁾, W₁ ⁽²⁾, W₁ ⁽⁴⁾, . . . , W₁ ⁽¹⁴⁾}; the sub-sampled C₂ is

$C_{2} = {{\left\{ {\begin{bmatrix} e_{1} & e_{1} \\ e_{1} & {- e_{1}} \end{bmatrix},\begin{bmatrix} e_{1} & e_{1} \\ {j\; e_{1}} & {{- j}\; e_{1}} \end{bmatrix}} \right\}\mspace{14mu}{for}\mspace{14mu} r} = 2.}$ and the sub-sampled C₂ is

$C_{2} = {{\left\{ {\begin{bmatrix} e_{1} & e_{1} \\ e_{1} & {- e_{1}} \end{bmatrix},\begin{bmatrix} e_{1} & e_{1} \\ {j\; e_{1}} & {{- j}\; e_{1}} \end{bmatrix}} \right\}\mspace{14mu}{for}\mspace{14mu} r} = 2.}$

According to another embodiment of the invention, in the sub-sampling, codewords evenly distributed in the codebook C are extracted, where some or all of the codewords are in a form of discrete Fourier transform (DFT) vector to be suitable for evenly linear arrays, and the other codewords are suitable for cross-polarized linear arrays.

Next, the method for sub-sampling of the codebook in the LTE-A system according to embodiments of the invention is further described in connection with the detailed embodiments of the invention.

Sub-Sampling Scheme for CSI Mode 1-1 According to Embodiments of the Invention

In the following, the sub-sampling schemes of rank 1-4 for CSI mode 1-1 are presented according to embodiments of the invention.

1. Sub-Sampling of Rank 3 or 4 Codebook

In order to achieve the nesting property of rank 3-7 codebooks, sub-sampling of rank 3 or 4 codebooks are proposed as follows. Note that since the rank 8 codebook corresponds to only one codeword, the nesting property thereof is unnecessary to be considered.

rank 3 or 4: the first codebook C₁ is the same as the above-mentioned original 2 bits codebook, while the second codebook C₂ is sub-sampled as:

when rank=3,

$\begin{matrix} {{{{{Codebook}\mspace{14mu} 2\text{:}\mspace{14mu} C_{2}} = \left\{ {\frac{1}{\sqrt{2}}\begin{bmatrix} Y_{1} & Y_{2} \\ Y_{1} & {- Y_{2}} \end{bmatrix}} \right\}}\left( {Y_{1},Y_{2}} \right) \in \left\{ {\left( {e_{1},\left\lbrack {e_{1},e_{5}} \right\rbrack} \right),\left( {e_{2},\left\lbrack {e_{2},e_{6}} \right\rbrack} \right),\left( {e_{3},\left\lbrack {e_{3},e_{7}} \right\rbrack} \right),\left( {e_{4},\left\lbrack {e_{4},e_{8}} \right\rbrack} \right)} \right\}};} & (5) \end{matrix}$

when rank=4,

$\begin{matrix} {{{{Codebook}\mspace{14mu} 2\text{:}\mspace{14mu} C_{2}} = \left\{ {\frac{1}{\sqrt{2\;}}\begin{bmatrix} Y & Y \\ Y & {- Y} \end{bmatrix}} \right\}}{Y \in {\left\{ {\left\lbrack {e_{1},e_{5}} \right\rbrack,\left\lbrack {e_{2},e_{6}} \right\rbrack,\left\lbrack {e_{3},e_{7}} \right\rbrack,\left\lbrack {e_{4},e_{8}} \right\rbrack} \right\}.}}} & (6) \end{matrix}$

The sub-sampled rank 3 and rank 4 codebooks obtained in this sub-sampling manner may have a nesting property together with the corresponding sub-sampled rank 1 and rank 2 codebooks having nesting property as well as rank 5-7 codebooks. This nesting property is very important for precoding, since base stations may acquire codeword information for various ranks according to the feedback PMI.

2. Sub-Sampling of Rank 1 or 2 Codebooks

As to sub-sampling of rank 1 or 2 codebooks, there may by a number of solutions to extract 16 codewords evenly distributed in the 256 codewords of codebook C. However, the sampling according to embodiments of the invention should obey the following principles:

(1) Due to the 4-bit limit in CSI mode 1-1, with sub-sampling there are at most 16 4TxDFT beams for X in W1 design.

(2) Accordingly, the sub-sampling scheme may select from C₁ 16 or 8 or 4 4TxDFT beams for X.

(3) Furthermore, W1*W2 may generate at least 4 8TxDFT vectors, which is suitable for evenly linear arrays.

Next, some examples for sub-sampling rank 1 or 2 codebooks are provided. For rank r, codeword (m,n)_(r) represents a codeword with rank r constructed by the multiplication of codeword with index m in C₁ and codeword with index n in C₂.

Sub-Sampling Scheme 1 for Rank 1 or 2 Codebooks

A 16-point 4-TxDFT for X is selected during design of W₁, and four 8-TxDFT vectors are generated from W₁ and W₂. These 8-TxDFT vectors are particularly suitable for evenly linear arrays, and the other 12 codewords in the sub-sampled codebook are suitable for cross-polarized arrays. With this sub-sampling and the sub-sampling for rank 3 or 4 as shown in equations (5) and (6), the sub-sampled codebooks with ranks 1 to 7 have the nesting property.

In this scheme, the first Codebook1 C₁ is the same as original 4 bits codebook, while the second Codebook2 C₂ is defined as:

${{{Rank}\mspace{14mu} 1\text{:}\mspace{14mu}{Codebook}\mspace{14mu} 2\text{:}\mspace{14mu} C_{2}} = \left\{ \begin{bmatrix} e_{1} \\ e_{1} \end{bmatrix} \right\}},{{{Rank}\mspace{14mu} 2\text{:}\mspace{14mu}{Codebook}\mspace{14mu} 2\text{:}\mspace{14mu} C_{2}} = {\left\{ \begin{bmatrix} e_{1} & e_{1} \\ e_{1} & {- e_{1}} \end{bmatrix} \right\}.}}$

Thereby, the sub-sampled codewords may be indexed as follows.

Rank 1: (0,0)₁, (1,0)₁, (2,0)₁, (3,0)₁, (4,0)₁, (5,0)₁, (6,0)₁, (7,0)₁, (8,0)₁, (9,0)₁, (10,0)₁, (11,0)₁, (12,0)₁, (13,0)₁, (14,0)₁, (15,0)₁

Rank 2: (0,0)₂, (1,0)₂, (2,0)₂, (3,0)₂, (4,0)₂, (5,0)₂, (6,0)₂, (7,0)₂, (8,0)₂, (9,0)₂, (10,0)₂, (11,0)₂, (12,0)₂, (13,0)₂, (14,0)₂, (15,0)₂.

Sub-Sampling Scheme 2 for Rank 1 or 2 Codebooks

A 16-point 4-TxDFT for X is selected during design of W₁, and sixteen 8-TxDFT vectors are generated from W₁ and W₂.

The sub-sampled codewords may be indexed as follows.

Rank 1: (0,0)₁, (1,1)₁, (2,2)₁, (3,3)₁, (4,0)₁, (5,1)₁, (6,2)₁, (7,3)₁, (8,0)₁, (9,1)₁, (10,2)₁, (11,3)₁, (12,0)₁, (13,1)₁, (14,2)₁, (15,3)₁

Rank 2: (0,0)₂, (1,1)₂, (2,0)₂, (3,1)₂, (4,0)₂, (5,1)₂, (6,0)₂, (7,1)₂, (8,0)₂, (9,1)₂, (10,0)₂, (11,1)₂, (12,0)₂, (13,1)₂, (14,0)₂, (15,1)₂.

Sub-Sampling Scheme 3 for Rank 1 or 2 Codebooks

A 8-point 4-TxDFT for X is selected during design of W₁, and four 8-TxDFT vectors are generated from W₁ and W₂.

The first codebook Codebook 1: C₁={W₁ ⁽⁰⁾, W₁ ⁽²⁾, W₁ ⁽⁴⁾, . . . , W₁ ⁽¹⁴⁾};

${{Rank}\mspace{14mu} 1\text{:}\mspace{14mu}{Codebook}\mspace{14mu} 2\text{:}\mspace{14mu} C_{2}} = \left\{ {\begin{bmatrix} e_{1} \\ e_{1} \end{bmatrix},\begin{bmatrix} e_{1} \\ {j\; e_{1}} \end{bmatrix}} \right\}$ ${{Rank}\mspace{14mu} 2\text{:}\mspace{14mu}{Codebook}\mspace{14mu} 2\text{:}\mspace{14mu} C_{2}} = \left\{ {\begin{bmatrix} e_{1} & e_{1} \\ e_{1} & {- e_{1}} \end{bmatrix},\begin{bmatrix} e_{1} & e_{1} \\ {j\; e_{1}} & {{- j}\; e_{1}} \end{bmatrix}} \right\}$

Thereby the sub-sampled codewords may be indexed as follows.

Rank 1: (0,0)₁, (0,1)₁, (2,0)₁, (2,1)₁, (4,0)₁, (4,1)₁, (6,0)₁, (6,1)₁, (8,0)₁, (8,1)₁, (10,0)₁, (10,1)₁, (12,0)₁, (12,1)₁, (14,0)₁, (14,1)₁

Rank 2: (0,0)₂, (0,1)₂, (2,0)₂, (2,1)₂, (4,0)₂, (4,1)₂, (6,0)₂, (6,1)₂ (8,0)₂, (8,1)₂, (10,0)₂, (10,1)₂, (12,0)₂, (12,1)₂, (14,0)₂, (14,1)₂.

From the above description, it is apparent that the method and apparatus for sub-sampling a codebook in the LTE-A system according to embodiments of the invention is easily to be obtained from the original codebooks prescribed in the protocol, and may have good nesting property as well as high spatial resolution. Further, the method and apparatus for sub-sampling a codebook in the LTE-A system according to embodiments of the invention is suitable for precoding data by LTE advanced base station and user equipment (UE).

The foregoing is described with respect to embodiments of the invention, however, the present invention is not limited to any specific methods or apparatuses. Various change or modification can be made by the skilled in the art without departing from the scope of the appended claims. 

What is claimed is:
 1. A method for sub-sampling of a codebook in a LTE-A system, the method comprising: receiving at a base station a precoding matrix W as a product of two matrices W₁ and W₂, wherein W=W₁W₂, and codebooks for W, W₁ and W₂ are denoted as C, C₁ and C₂ respectively, and r indicates a rank; the base station sub-sampling the codebook C by applying the following equations under the following circumstances such that the sub-sampled codebook C has a size of equal to or less than 4 bits, wherein when the received codebook has an r=1 or 2, C₁ has the size of 4 bits and for a given codeword in C₁, one codeword in C₂ corresponds; wherein when the received codebook has a value of r=3 or 4, C₁ has a size of 2 bits and C₂ is subsampled as: $\begin{matrix} {{{C_{2} = {{\left\{ {\frac{1}{\sqrt{2}}\begin{bmatrix} Y_{1} & Y_{2} \\ Y_{1} & {- Y_{2}} \end{bmatrix}} \right\}\mspace{14mu}{for}\mspace{14mu} r} = 3}}\left( {Y_{1},Y_{2}} \right) \in \left\{ {\left( {e_{1},\left\lbrack {e_{1},e_{5}} \right\rbrack} \right),\left( {e_{2},\left\lbrack {e_{2},e_{6}} \right\rbrack} \right),\left( {e_{3},\left\lbrack {e_{3},e_{7}} \right\rbrack} \right),\left( {e_{4},\left\lbrack {e_{4},e_{8}} \right\rbrack} \right)} \right\}};} & (1) \\ {{C_{2} = {{\left\{ {\frac{1}{\sqrt{2}}\begin{bmatrix} Y & Y \\ Y & {- Y} \end{bmatrix}} \right\}\mspace{14mu}{for}\mspace{14mu} r} = 4}}{{Y \in \left\{ {\left\lbrack {e_{1},e_{5}} \right\rbrack,\left\lbrack {e_{2},e_{6}} \right\rbrack,\left\lbrack {e_{3},e_{7}} \right\rbrack,\left\lbrack {e_{4},e_{8}} \right\rbrack} \right\}};}} & (2) \end{matrix}$ Yε{[e₁,e₅],[e₂,e₆],[e₃,e₇],[e₄,e₈]} where e_(k) indicates an 8×1 selection vector for which the k-th element has a value of 1 and the other elements are zero, and the sub-sampled rank 3 codebook and rank 4 codebook have a nesting property; and wherein when the received codebook has a value of r=1 or 2, and C₂ is sub-sampled to 1 bit, C₁ is sub-sampled to 3 bits, wherein the sub-sampled C₁ is C₁={W₁ ⁽⁰⁾, W₁ ⁽²⁾, W₁ ⁽⁴⁾, . . . , W₁ ⁽¹⁴⁾} such that the sampled C₂ is ${C_{2} = {{\left\{ {\begin{bmatrix} e_{1} \\ e_{1} \end{bmatrix},\begin{bmatrix} e_{1} \\ {j\; e_{1}} \end{bmatrix}} \right\}\mspace{14mu}{for}\mspace{14mu} r} = 1}},$ and the sampled C₂ is $C_{2} = {{\left\{ {\begin{bmatrix} e_{1} & e_{1} \\ e_{1} & {- e_{1}} \end{bmatrix},\begin{bmatrix} e_{1} & e_{1} \\ {j\; e_{1}} & {{- j}\; e_{1}} \end{bmatrix}} \right\}\mspace{14mu}{for}\mspace{14mu} r} = 2.}$
 2. The method of claim 1, wherein when the received codebook has a value of r=1 or 2, C₁ is sub-sampled to 4 bits, and C₂ is defined as: the sub-sampled C₂ is ${C_{2} = {{\left\{ \begin{bmatrix} e_{1} \\ e_{2} \end{bmatrix} \right\}\mspace{14mu}{for}\mspace{14mu} r} = 1}},$ and the sub-sampled C₂ is ${C_{2} = {{\left\{ \begin{bmatrix} e_{1} & e_{1} \\ e_{1} & {- e_{1}} \end{bmatrix} \right\}\mspace{14mu}{for}\mspace{14mu} r} = 2}},$ wherein e₁ indicates a 4×1 selection vector for which the first element has a value of 1 and the other elements are zero, and the sub-sampled rank 1 codebook, rank 2 codebook and the corresponding rank 3 code-book and rank 4 codebook have a nesting property.
 3. The method of claim 1, wherein, when the received codebook has a value of r=1, for a codeword W₁ ^((4k+l)) in C₁, k=0, 1, 2, 3, l=0, 1, 2, 3, a codeword $\frac{1}{\sqrt{2}}\begin{bmatrix} e_{1} \\ {\alpha_{l}e_{1}} \end{bmatrix}$ in C₂ is extracted to correspond thereto, wherein e₁ indicates a 4×1 selection vector for which the first element has a value of 1 and the other elements are zero, and α₀=1, α₁=j, α₂=−1 and α₃=−j; and when the received codebook has a value of r=2, for a codeword W₁ ^((2k+l)) in C₁, k=0, 1, . . . , 7, l=0, 1, a codeword $\frac{1}{\sqrt{2}}\begin{bmatrix} e_{1} & e_{1} \\ {\alpha_{l}e_{1}} & {{- \alpha_{l}}e_{1}} \end{bmatrix}$ in C₂ is extracted to correspond thereto, wherein α₀=1, α₁=j.
 4. An apparatus for sub-sampling of a codebook in a LTE-A system where a precoding matrix W is a product of two matrices W₁ and W₂, wherein W=W₁W₂, codebooks for W, W₁ and W₂ are denoted as C, C₁ and C₂ respectively, and r indicates a rank, the apparatus comprising: a processor configured to sub-sample the received codebook C, the received sub-sampled codebook C has a size of equal to or less than 4 bits; and a receiver configured to receive the sub-sampled codebook C for precoding in an LTE advanced base station and/or user equipment, wherein when r=1 or 2, C₁ has the size of 4 bits and for a given codeword in C₁, one codeword in C₂ corresponds thereto; wherein r=3 or 4 C₁ has a size of 2 bits and the processor sub-samples C₂ as: $\begin{matrix} {\mspace{79mu}{{C_{2} = {{\left\{ {\frac{1}{\sqrt{2}}\begin{bmatrix} Y_{1} & Y_{2} \\ Y_{1} & {- Y_{2}} \end{bmatrix}} \right\}\mspace{14mu}{for}\mspace{14mu} r} = 3}}{{\left( {Y_{1},Y_{2}} \right) \in \left\{ {\left( {e_{1},\left\lbrack {e_{1},e_{5}} \right\rbrack} \right),\left( {e_{2},\left\lbrack {e_{2},e_{6}} \right\rbrack} \right),\left( {e_{3},\left\lbrack {e_{3},e_{7}} \right\rbrack} \right),\left( {e_{4},\left\lbrack {e_{4},e_{8}} \right\rbrack} \right)} \right\}};}}} & (1) \\ {\mspace{79mu}{{C_{2} = {{\left\{ {\frac{1}{\sqrt{2}}\begin{bmatrix} Y & Y \\ Y & {- Y} \end{bmatrix}} \right\}\mspace{14mu}{for}\mspace{14mu} r} = 4}}\mspace{79mu}{{Y \in \left\{ {\left\lbrack {e_{1},e_{5}} \right\rbrack,\left\lbrack {e_{2},e_{6}} \right\rbrack,\left\lbrack {e_{3},e_{7}} \right\rbrack,\left\lbrack {e_{4},e_{8}} \right\rbrack} \right\}};}}} & (2) \end{matrix}$ wherein e_(k) indicates an 8×1 selection vector for which the k-th element has a value of 1 and the other elements are zero, and the sub-sampled rank 3 codebook and rank 4 codebook have a nesting property; and wherein when r=1 or 2, the processor is configured to sub-sample C₁ and C₂ respectively, and C₂ is sub-sampled to 1 bit, C₁ is sub-sampled respectively to 3 bits, wherein the processor sub-samples C₁ as C₁={W₁ ⁽⁰⁾, W₁ ⁽²⁾, W₁ ⁽⁴⁾, . . . , W₁ ⁽¹⁴⁾} such that the processor samples C₂ as ${C_{2} = {{\left\{ {\begin{bmatrix} e_{1} \\ e_{1} \end{bmatrix},\begin{bmatrix} e_{1} \\ {j\; e_{1}} \end{bmatrix}} \right\}\mspace{14mu}{for}\mspace{14mu} r} = 1}},$ and the processor samples C₂ as $C_{2} = {{\left\{ {\begin{bmatrix} e_{1} & e_{1} \\ e_{1} & {- e_{1}} \end{bmatrix},\begin{bmatrix} e_{1} & e_{1} \\ {j\; e_{1}} & {{- j}\; e_{1}} \end{bmatrix}} \right\}\mspace{14mu}{for}\mspace{14mu} r} = 2.}$
 5. The apparatus of claim 4, wherein when r=1 or 2, C₁ is sub-sampled to 4 bits, and the processor is configured to define C₂ as: ${C_{2} = {{\left\{ \begin{bmatrix} e_{1} \\ e_{1} \end{bmatrix} \right\}\mspace{14mu}{for}\mspace{14mu} r} = 1}},$ and ${C_{2} = {{\left\{ \begin{bmatrix} e_{1} & e_{1} \\ e_{1} & {- e_{1}} \end{bmatrix} \right\}\mspace{14mu}{for}\mspace{14mu} r} = 2}},$ wherein e₁ indicates a 4×1 selection vector for which the first element has a value of 1 and the other elements are zero, and the sub-sampled rank 1 codebook, rank 2 codebook and the corresponding rank 3 code book and rank 4 codebook have a nesting property.
 6. The apparatus of claim 4, wherein when r=1, for a codeword W₁ ^((4k+l)) in C₁, k=0, 1, 2, 3, l=0, 1, 2, 3, the processor extracts a codeword $\frac{1}{\sqrt{2}}\begin{bmatrix} e_{1} \\ {\alpha_{l}e_{1}} \end{bmatrix}$ in C₂ to correspond thereto, wherein e₁ indicates a 4×1 selection vector for which the first element has a value of 1 and the other elements are zero, and α₀=1, α₁=j, α₂=−1 and α₃=−j; and when r=2, for a codeword W₂ ^((2k+l)) in C₁, k=0, 1, . . . , 7, l=0, 1, the processor extracts a codeword $\frac{1}{\sqrt{2}}\begin{bmatrix} e_{1} & e_{1} \\ {\alpha_{l}e_{1}} & {{- \alpha_{l}}e_{1}} \end{bmatrix}$ in C₂ to correspond thereto, wherein α₀=1, α₁=j. 